President Barack Obama set the stage in November when he announced new executive actions (now tied up in court) to prevent the deportation of millions of unauthorized immigrants, expanding 2012’s original program aimed mostly at providing relief to those brought to the United States as children. Illegal immigration has dominated the Republican presidential campaign, particularly after Donald Trump’s call for deporting all undocumented immigrants in the U.S. and building a wall along the U.S.-Mexico border. Others have called for a changing the constitutional amendment that guarantees birthright citizenship.

Among the public overall, there is little support for an effort to deport all those in the U.S. illegally, but surveys in past years have found greater support for building a barrier along the Mexican border and for changing the Constitution to ban birthright citizenship.

Republicans have long been conflicted over U.S. immigration policy. On the one hand, consistent majorities of Republicans favor providing a path to legal status for people in the U.S. illegally. Yet most Republicans also worry that granting legal status to undocumented immigrants would amount to a tacit reward for illegal behavior. And in the past, nearly half of Republicans supported changing the Constitution to bar birthright citizenship, and a majority supported building a fence along the entire U.S. border with Mexico.

Here’s a breakdown of public opinion on some key immigration issues:

Stay or deport? In a Pew Research Center survey conducted in May, a solid majority (72%) of Americans – including 80% of Democrats, 76% of independents and 56% of Republicans – say undocumented immigrants currently living in the U.S.should be allowed to stay in this country legally if they meet certain requirements. Last year, we asked a follow-up question of those who opposed granting legal status to undocumented immigrants: Should there be a “national law enforcement effort to deport” all immigrants here illegally? Just 17% of the public overall favored such an effort, including about a quarter (27%) of Republicans.

Moreover, in a 2013 survey, 76% of Republicans said that deporting all immigrants in the U.S. illegally was “unrealistic.”

One measure of public sentiment is how Americans have felt about the record number of deportations of unauthorized immigrants during the Obama administration – and an early-2014 survey found the public was divided. Overall, 45% of Americans called the increase in such deportations a good thing and the same share said it was a bad thing. Republicans (55% good thing), especially Republicans and Republican leaners who agree with the Tea Party (65%), were more likely than Democrats (37%) to have a positive view of increased deportations.

A majority (60%) of Hispanics saw the increase in deportations as a bad thing. In another survey of Latino adults in 2013, nearly half (46%) said they worry “a lot” or “some” that they, a family member or a close friend could be deported. And 56% said it was more important for undocumented immigrants to be able to work and live in the U.S. without the threat of deportation than to obtain a pathway to citizenship, according to our 2014 poll.

At that time, the idea of ending birthright citizenship drew broad opposition among Hispanics (73%), young people (73% of those under 30) and Democrats (66%). However, Republicans were divided: 49% wanted to leave the Constitution as it is, while 47% favored a constitutional amendment to bar birthright citizenship.

In 2012, at least 4.5 million U.S.-born children lived with at least one unauthorized parent, according to our analysis. Some 4 million unauthorized immigrant adults lived with their U.S.-born children.

Build a wall, or a fence: Our most recent survey on this issue was in October 2011. At that time, 46% favored building a fence “along the entire border with Mexico,” while 47% were opposed. Republicans (62%) were far more likely than independents (44%) or Democrats (39%) to support the construction of a border fence.

Overall views of immigrants: Views about immigration policies are often shaped by views about immigrants themselves: Are immigrants generally a problem, taking jobs and services, or do they strengthen the country through hard work and talents?

In our May survey, about half of Americans (51%) say immigrants strengthen the country, while 41% view them as a burden. (These opinions have fluctuated over the years, but in the mid-1990s, majorities said immigrants to the U.S. were a burden.) However, Republicans (63%) are far more likely than Democrats (32%) to say immigrants are a burden. And the share of Republicans who regard immigrants as a burden jumped 15 percentage points, from 48% in March 2014.

Declining immigration: The latest immigration debate comes against a backdrop in which the number of unauthorized immigrants coming to the U.S. has leveled off. That number peaked in 2007, especially for those from Mexico.

As growth of this group has stalled, there has been a recent sharp rise in the median length of time that unauthorized immigrants have lived in the U.S. In 2013, unauthorized immigrant adults had been in the U.S. for a median time of nearly 13 years – meaning that half had been in the country at least that long, according to a preliminary estimate. A decade earlier, in 2003, the median for adults was less than eight years.

Despite the renewed focus on immigration, it’s worth keeping in mind that immigrationhas not ranked high in our annual poll on the issues Americans see as a top priority for the president and Congress. Even among Hispanics, immigration has not been a top priority; a 2014 survey found that Hispanics rated education (92%), jobs and the economy (91%), and health care (86%) as extremely or very important issues but fewer said the same about immigration (73%).